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Rates of change and differential equations — Question 16

QCAA 2025, Paper 2 · 6 marks

Q16 · 2025 · Technology-activeComplex familiar6 marks

QUESTION 16 (6 marks)

A certain population can be approximately modelled by the differential equation dPdt=0.5P(1−0.2P)\frac{dP}{dt}=0.5P(1-0.2P) where PP is the population in millions and tt is the number of years since 1 January 2025. Given that the population on 1 January 2025 was estimated at 0.3 million, use a calculus approach to estimate the population on 1 January 2030.
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